An infinity series involving the Smarandache-type function

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give several interesting identities for it

Information Structures with Unawareness

I construct a state space model with unawareness following Aumann (1976). Dekel, Lipman and Rustichini (1998a) show that standard state space models are incapable of representing unawareness. The model circumvents the impossibility result by endowing the agent with a subjective state space that differs from the full state space when he has the unawareness problem. Information is modeled as a pair, consisting of both factual information and awareness information. The model preserves the central properties of the standard information partition model.unawareness, information, information partition, state space models

Modeling Unawareness in Arbitrary State Spaces

I develop a set-theoretic model of unawareness without making any structural assumptions on the underlying state space. Unawareness is characterized as a measurability constraint that results in players' reasoning about a “coarse" subjective algebra of events. The model is shown to be essentially equivalent to the product model in Li (2007), indicating that such a measurability constraint can be captured by restrictions on the dimensions of the state space without loss of generality. I use a variant of the partition model to examine the case of partial unawareness, where the player is aware of a question but unaware of some possible answers to that question, and characterize the player's knowledge hierarchies from his subjective perspective.unawareness, partial unawareness, information, information partition, the state space

Active Longitudes Revealed by Large-scale and Long-lived Coronal Streamers

We use time-series ultraviolet full sun images to construct limb-synoptic maps of the Sun. On these maps, large-scale, long-lived coronal streamers appear as repetitive sinusoid-like arcs projected over the polar regions. They are caused by high altitude plasma produced from sunspot-rich regions at latitudes generally far from the poles. The non-uniform longitudinal distribution of these reveals four longitudinal zones at the surface of the sun from which sunspots erupt preferentially over the 5-year observing interval (2006 January to 2011 April). Spots in these zones (or "clusters") have individual lifetimes short compared to the lifetimes of the coronal features which they sustain, and erupt at different times. The four sunspot clusters contain >75% of all numbered sunspots in this period. They occupy two distinct longitudinal zones separated by ~180 degree and each spanning ~100 degree in longitude. The rotation rates of the spot clusters are ~5% faster than the rates at both the surface and the bottom of the convection zone. While no convincing theoretical framework exists to interpret the sunspot clusters in the longitude-time space, their persistent and nonuniform distribution indicates long-lived, azimuthal structures beneath the surface, and are compatible with the existence of previously-reported active longitudes on the sun.Comment: 26 pages, 8 figures, Accepted by ApJ 2011 April 28, http://www2.ess.ucla.edu/~jingli/ApJ201104

Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0)

In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 01, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is evaluated. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1208.3672, arXiv:1208.351

Vitality and Modernity: Defining the “Folk” in Early Twentieth Century China

As usual, the 2005 Chinese Rooster New Year celebrations in Beijing highlighted the annual Earth Temple Fair (Ditan Miaohui) as an indispensable attraction. In recent years, this entertaining space featuring red lanterns, lion dances, and revived folk performances has been widely and officially advocated as an occasion and place to appreciate “national culture (minzu wenhua)” and to experience “folk culture (minsu wenhua).” In the commodified and globalized metropolitan capital of the nation, the Fair forms a symbolic space where traditionality is celebrated to label national identity. [excerpt

China\u27s New Labor Contract Law and Protection of Workers

This Comment will discuss the labor conditions in China that prompted many provisions in the recently enacted Labor Contract Law, and how the new law responds to deficiencies of China\u27s Labor Law to address various labor problems. Part I of this Comment contains a brief presentation of the historical and economic background of the emergence of migrant workers. Part I also examines the causes of the main problems faced by migrant workers, in particular the insufficiencies of China\u27s Labor Law in protecting migrant workers. Part II looks into the legislation\u27s background and specific provisions of China\u27s new Labor Contract Law that supplement the Labor Law and stress the protection of laborers. Many provisions of the new law specifically address labor abuses faced by migrant workers. Finally, Part III discusses the insufficiencies and likely effects of the new Labor Contract Law